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%I #8 Aug 25 2023 09:43:14
%S 1,1,10,201,6220,261465,13925286,898994383,68240292856,5956670911041,
%T 587896878021130,64738492669538391,7869297152389747284,
%U 1046629627952327990545,151192146681811716344878,23573456446401808474471455,3945806733850334447131941616
%N E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^3).
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3*n+k+1,k)/( (3*n+k+1)*(n-k)! ).
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n+k+1, k)/((3*n+k+1)*(n-k)!));
%Y Cf. A364987, A364989, A365175, A365176.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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